Related papers: Coins and Logic
I introduce, solve and generalize a new coin puzzle that involves parallel weighings.
We discuss some old common knowledge puzzles and introduce a lot of new common knowledge puzzles.
Knights and knaves problems represent a classic genre of logical puzzles where characters either tell the truth or lie. The objective is to logically deduce each character's identity based on their statements. The challenge arises from the…
We provide here a dataset for tasks related to natural language understanding and natural language inference. The dataset contains logical puzzles in natural language from three domains: comparing puzzles, knighs and knaves, and zebra…
We investigate a coin-weighing puzzle that appeared in the all-Russian math Olympiad in 2000. We liked the puzzle because the methods of analysis differ from classical coin-weighing puzzles. We generalize the puzzle by varying the number of…
We discuss ``puzzles of prisoners and hats`` with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of…
We investigate a coin-weighing puzzle that appeared in the Moscow Math Olympiad in 1991. We generalize the puzzle by varying the number of participating coins, and deduce an upper bound on the number of weighings needed to solve the puzzle…
We discuss coin-weighing problems with a new type of coin: a chameleon. A chameleon coin can mimic a fake or a real coin, and it can choose which coin to mimic for each weighing independently. We consider a mix of $N$ coins that include…
We study the famous mathematical puzzle of prisoners and hats. We introduce a framework in which various variants of the problem can be formalized. We examine three particular versions of the problem (each one in fact a class of problems)…
We introduce a new family of one-player games, involving the movement of coins from one configuration to another. Moves are restricted so that a coin can be placed only in a position that is adjacent to at least two other coins. The goal of…
Riddles are concise linguistic puzzles that describe an object or idea through indirect, figurative, or playful clues. They are a longstanding form of creative expression, requiring the solver to interpret hints, recognize patterns, and…
We discuss games involving a counterfeit coin. Given one counterfeit coin among a number of otherwise identical coins, two players with full knowledge of the fake coin take turns weighing coins on a two-pan scale, under the condition that…
We investigate the complexity of a puzzle that turns out to be NL-complete.
Riddles based on simple puns can be classified according to the patterns of word, syllable or phrase similarity they depend upon. We have devised a formal model of the semantic and syntactic regularities underlying some of the simpler types…
The procedure of tossing quantum coins and dice is described. This case is an important example of a quantum procedure because it presents a typical framework employed in quantum information processing and quantum computing. The emphasis is…
Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs'…
Connections between the sequentiality/concurrency distinction and the semantics of proofs are investigated, with particular reference to games and Linear Logic.
We discuss fun problems, vaguely related to notions and theorems of a course in differential geometry. This paper can be regarded as a weekend "treasure chest" supplementing the course weekday lecture notes. The problems and solutions are…
We present an analysis of a coin-tossing problem posed by Daniel Litt which has generated some popular interest. We demonstrate a recursive identity which leads to relatively simple formulas for the excess number of wins for one player over…
We present in this paper our solver for logic grid puzzles. The approach used by our algorithm mimics the way a human would try to solve the same problem. Every progress made during the solving process is accompanied by a detailed…